I suggest that you cook them up in this recipe...(I know that you did not ask for recipes but this really is great!)...it calls for cherry tomatoes, but believe me, the grape tomatoes work just beautifully...they get all blackened and oogey and delicious--you can easily sub fresh basil if you don't have marjoram, fresh oregano works nicely too:

I really think the places I buy from have high turnover and put a premium on their produce. So it's hard to think they are selling stuff that is not pretty fresh.

I don't refrigerate regular tomatoes (of course!) but I do refrigerate the cherry and grape tomatoes. Do you think that could be the problem? Mine are definitely not lasting 6 days. The reason I started doing that was I didn't think refrigerating these was affecting the taste.

I could do an experiment with my next batch and refrigerate half and leave half out. And do another one with the glass jar.